Wireless telephones, such as mobile/cellular telephones, cordless telephones, and other consumer audio devices, such as mp3 players, are in widespread use. Performance of such devices with respect to intelligibility can be improved by providing noise canceling using a microphone to measure ambient acoustic events and then using signal processing to insert an anti-noise signal into the output of the device to cancel the ambient acoustic events. Because the acoustic environment around personal audio devices such as wireless telephones can change dramatically, depending on the sources of noise that are present and the position of the device itself, it is desirable to adapt the noise canceling to take into account such environmental changes.
Adaptive noise cancellation may be used in many elements of personal audio devices, including headphones. Headphones that provide adaptive noise cancellation to a listener may also be used to play audio content to the headphones in a variety of cases. For example, in a phone call, audio content may occupy a telephone speech band of between 300 Hz and 3.4 kHz, inclusive, or in a high-fidelity audio playback situation, the audio content may occupy a frequency range of 20 Hz to 20 kHz, inclusive, for some audio tracks, or 100 Hz to 8 kHz for some compressed audio content. An adaptive noise cancellation system must be stable under all conditions, regardless of the bandwidth of the ambient noise or the bandwidth of a source audio signal. Any adaptive system that depends on a model of an electro-acoustic path of the source audio signal through a transducer, for example a filtered-X least-mean-square feedforward adaptive system, must comprehend the frequency spectra of the various signals involved in such a way that instability in adaptation is avoided.